Revista Integración, temas de matemáticas.
Vol. 33 Núm. 2 (2015): Revista Integración, temas de matemáticas
Artículos científicos

Extensiones PBW torcidas de anillos de Baer, quasi-Baer, p.p. y p.q-Baer

Armando Reyes
Universidad Nacional de Colombia

Publicado 2015-12-04

Palabras clave

  • Anillos Baer,
  • quasi-Baer,
  • p.p,
  • p.q.-Baer,
  • extensiones torcidas de Poincaré-Birkhoff-Witt.

Cómo citar

Reyes, A. (2015). Extensiones PBW torcidas de anillos de Baer, quasi-Baer, p.p. y p.q-Baer. Revista Integración, Temas De matemáticas, 33(2), 173–189. https://doi.org/10.18273/revint.v33n2-2015007

Resumen

El propósito de este artículo es estudiar las extensiones torcidas de Poincaré-Birkhoff-Witt de anillos de Baer, quasi-Baer, p.p. y p.q.-Baer. Utilizando una noción de rigidez, probamos que estas propiedades son estables para esta clase de extensiones.

Para citar este artículo: A. Reyes, Skew PBW Extensions of Bear, quasi-Baer, p.p. and p.q.-rings, Rev. Integr. Temas Mat. 33 (2015), No. 2, 173–189.

 

Descargas

Los datos de descargas todavía no están disponibles.

Referencias

  1. Armendariz E.P., “A note on extensions of Baer and p.p.-rings”, J. Austral. Math. Soc. 18 (1974), 470–473.
  2. Armendariz E.P., Koo H.K. and Park J.K., “Isomorphic Ore extensions”, Comm. Algebra 15 (1987), No. 12, 2633–2652.
  3. Birkenmeier G.F., “Baer rings and quasicontinuous rings have a MDSN”, Pacific J. Math. 97 (1981), No. 2, 283–292.
  4. Birkenmeier G.F., Kim J.Y. and Park J.K., “Principally quasi-Baer rings”, Comm. Algebra 29 (2001), No. 2, 639–660.
  5. Birkenmeier G.F., Kim J.Y. and Park J.K., “Polynomial extensions of Baer and quasi-Baer rings”, J. Pure Appl. Algebra 159 (2001), No. 1, 25–42.
  6. Clark W.E., “Twisted matrix units semigroup algebras”, Duke Math. J. 34 (1967), 417–423.
  7. Gallego C. and Lezama O., “Gröbner bases for ideals of σ-PBW extensions”, Comm. Algebra 39 (2011), No. 1, 50–75.
  8. Han J., Hirano Y. and Kim H., “Semiprime Ore extensions”, Comm. Algebra 28 (2000), No. 8, 3795–3801.
  9. Han J., Hirano Y. and Kim H., “Some results on skew polynomial rings over a reduced ring”, in International Symposium on Ring Theory (Kyongju, 1999), Trends Math., Birkhäuser Boston, Boston, MA (2001), 123–129.
  10. Hashemi E., Moussavi A. and Seyyed Javadi H.H., “Polynomial Ore extensions of Baer and p.p.-rings”, Bull. Iranian Math. Soc. 29 (2003), No. 2, 65–86.
  11. Hashemi E. and Moussavi A., “Polynomial extensions of quasi-Baer rings”, Acta Math. Hungar. 107 (2005), No. 3, 207–224.
  12. Hinchcliffe O., “Difussion Algebras”, Thesis (Ph.D.), University of Sheffield, Sheffield, 2005, 118 p.
  13. Hong C.Y., Kim N.K. and Kwak T.K., “Ore extensions of Baer and p.p.-rings”, J. Pure Appl. Algebra 151 (2000), No. 3, 215–226.
  14. Hong C.Y., Kim N.K. and Lee Y., “Ore extensions of quasi-Baer rings”, Comm. Algebra 37 (2009), No. 6, 2030–2039.
  15. Kaplansky I., Rings of Operators. W.A. Benjamin, Inc., New York-Amsterdam, 1968.
  16. Krempa J., “Some Examples of reduced rings”, Algebra Colloq. 3 (1996), No. 4, 289–300.
  17. Lezama O. and Reyes A., “Some homological properties of skew PBW extensions”, Comm. Algebra 42 (2014), No. 3, 1200–1230.
  18. Lezama O., Acosta J.P. and Reyes A., “Prime ideals of skew PBW extensions”, Rev. Un. Mat. Argentina 56 (2015), No. 2, 39–55.
  19. Matczuk J., “A Characterization of σ-rigid rings”, Comm. Algebra 32 (2004), No. 11, 4333–4336.
  20. McConnell J.C. and Robson J.C., Noncommutative Noetherian rings, Graduate Studies in Mathematics, 30, American Mathematical Society, Providence, RI, 2001.
  21. Nasr-Isfahani A.R. and Moussavi A., “Baer and quasi-Baer differential polynomial rings”, Comm. Algebra 36 (2008), No. 9, 3533–3542.
  22. Passman D.S., “Prime ideals in enveloping rings”, Trans. Amer. Math. Soc. 302 (1987), No. 2, 535–560.
  23. Reyes A., “Ring and module theoretical properties of skew PBW extensions”, Thesis (Ph.D.), Universidad Nacional de Colombia, Bogotá, 2013, 142 p.
  24. Reyes A., “Jacobson’s conjecture and skew PBW extensions”, Rev. Integr. Temas Mat. 32 (2014), No. 2, 139 -152.